Mathematical problem

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Re: Mathematical problem

Post by musketeer925 »

@momuuu yeah I got a similar thing. I think the problem is that we need to calculate the value of the wine on the 14062th day, regardless of many days you take to gather it.

If we get done on the fourth day, we should be allowed to collect interest on it for the remaining 14062th day. Otherwise the 1 worker gets 14062 days worth of interest, but 14062 workers get 1 day worth of interest.
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Re: Mathematical problem

Post by musketeer925 »

I think with that change it's going to be "as many workers as possible", but I'm not sure yet.
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Re: Mathematical problem

Post by momuuu »

Aaaah, I get it. The problem with the exponential 1.007 is that profit is maximized if you play the game as long as possible. In other words, playing the game for an hour while fishing with one boat is more 'profitable' than playing for five minutes with 50 boats. After all, we're assuming in this mathematical simplification that the game simply stops when the food is all gathered up and profit equals the amount of res we gather in a game.
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Re: Mathematical problem

Post by momuuu »

musketeer925 wrote:@momuuu yeah I got a similar thing. I think the problem is that we need to calculate the value of the wine on the 14062th day, regardless of many days you take to gather it.

If we get done on the fourth day, we should be allowed to collect interest on it for the remaining 14062th day. Otherwise the 1 worker gets 14062 days worth of interest, but 14062 workers get 1 day worth of interest.

Yes, basically this. In this mathematical problem you just want to prolong getting interest, because interest is awesome.
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Re: Mathematical problem

Post by deleted_user0 »

musketeer925 wrote:I think with that change it's going to be "as many workers as possible", but I'm not sure yet.

That's not possible.

If you go above 180 workers, you have pay more than 9000 wine bottles. Even if they would gather it in 1 day, you would make loss compared to the original situation.
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Re: Mathematical problem

Post by deleted_user0 »

momuuu wrote:Aaaah, I get it. The problem with the exponential 1.007 is that profit is maximized if you play the game as long as possible. In other words, playing the game for an hour while fishing with one boat is more 'profitable' than playing for five minutes with 50 boats. After all, we're assuming in this mathematical simplification that the game simply stops when the food is all gathered up and profit equals the amount of res we gather in a game.

So basically we should set a time constraint to get reasonable results?
For example t< 600 ?
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Re: Mathematical problem

Post by musketeer925 »

somppukunkku wrote:
musketeer925 wrote:I think with that change it's going to be "as many workers as possible", but I'm not sure yet.

That's not possible.

If you go above 180 workers, you have pay more than 9000 wine bottles. Even if they would gather it in 1 day, you would make loss compared to the original situation.

Yeah, but I have an infinite pool of money that I can invest in workers, and then I can sell whenever I feel like it. So I invest enough in workers to gather it all on day 1, and then collect interest until I have enough to pay off the zero-interest loan from my infinite capital pool.

Basically we need to know on what day you want to cash out.

So basically we should set a time constraint to get reasonable results?
For example t< 600 ?

exactly
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Re: Mathematical problem

Post by momuuu »

musketeer925 wrote:I think with that change it's going to be "as many workers as possible", but I'm not sure yet.

In that case the number of days is constant and independent of the number of workers. If you refer to my calculation, that means we find a linear relation of profit = N * (some positive constant). So yes, as many workers as possible.
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Re: Mathematical problem

Post by musketeer925 »

I think there's something missing here. Spending half as much on workers and gathering over two days seems better than spending enough to gather on 1 day. The extra 1 day of interest on half of 9000 shouldn't cover the cost of doubling the workforce
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Re: Mathematical problem

Post by deleted_user0 »

@musketeer925

I'm really bad at explaining this but for example.

If you pay all your workers combined 10 000 wine bottles and they gather 9000 in one day (and workers are worthless after).
Those 10 000 wine bottles you pay are going to gain interest same time as 9000 gathered and you will be worse-off. Simply 1000 less bottles to gain value at any t.
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Re: Mathematical problem

Post by musketeer925 »

oh so you also pay the same interest on the negative wine bottles that you've spent?
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Re: Mathematical problem

Post by deleted_user0 »

Yes. That's the "opportunity cost".
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Re: Mathematical problem

Post by deleted_user0 »

Let's say you start with 9000 wine bottles and not infinite to make it clearer. And they would start "gathering" value immediately.
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Re: Mathematical problem

Post by momuuu »

No boats then.

Exponential increase is insane. Its probably not accurate for aoe3. In terms of aoe3 equivalents, you assume that our resources will eventually lead to a 10000 vill economy.
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Re: Mathematical problem

Post by deleted_user0 »

Yea. I get the point. 10k res at 70 mins is basically same as 10k res at 90 mins ingame.

However, what if we assume that t<300 and the game ends there?
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Re: Mathematical problem

Post by deleted_user0 »

oops, error, editing
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Re: Mathematical problem

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Now the problem is: How to write a math function to determine the outcome? With different constraints of t.
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Re: Mathematical problem

Post by momuuu »

somppukunkku wrote:Yea. I get the point. 10k res at 70 mins is basically same as 10k res at 90 mins ingame.

However, what if we assume that t<300 and the game ends there?

We find profit = N ( (92-50) 1.007^t - 93 )
So if t is small, its not profitable to make boats. Otherwise you should make as many as possible.

In this case this happens at x ~ 113.

I think the exponential increase is incorrect.
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Re: Mathematical problem

Post by momuuu »

somppukunkku wrote:Now the problem is: How to write a math function to determine the outcome? With different constraints of t.

If you fix t it turns into a linear function I think.
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Re: Mathematical problem

Post by deleted_user0 »

momuuu wrote:
somppukunkku wrote:Yea. I get the point. 10k res at 70 mins is basically same as 10k res at 90 mins ingame.

However, what if we assume that t<300 and the game ends there?

We find profit = N ( (92-50) 1.007^t - 93 )
So if t is small, its not profitable to make boats. Otherwise you should make as many as possible.

In this case this happens at x ~ 113.

I think the exponential increase is incorrect.

Yea. Exponential increase should decrease over time.
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Re: Mathematical problem

Post by musketeer925 »

I'm a little behind, but

Image

top line: 50 + interest on 50
bottom line: start w/ zero and gather at 0.64

the interest is always better with these numbers. With different interest rate and cost, you could see they might intersect, making gathering a good investment for a little while
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Re: Mathematical problem

Post by deleted_user0 »

musketeer925 wrote:I'm a little behind, but

Image

top line: 50 + interest on 50
bottom line: start w/ zero and gather at 0.64

the interest is always better

Counter example: You start with 9000 bottles.

im nub
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Re: Mathematical problem

Post by deleted_user0 »

Nerds... everyone knows the optimal amount of fishingboats is 21.
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Re: Mathematical problem

Post by musketeer925 »

but in scenario 1 you spent 35,000 day 1 bottles on hiring workers, which you didn't account for
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Re: Mathematical problem

Post by deleted_user0 »

musketeer925 wrote:but in scenario 1 you spent 35,000 bottles on hiring workers, which you didn't account for

oh fuck, i'm too tired haha. multiplied with wrong cost

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